I think that you would be hard pressed to feel any difference between various oils for lubrication on top of the piston in a fork. Cheapest option is whatever engine oil you have sitting around for your car. Synthetic or regular oil, thick or thin, it is not going to matter. You don't need anything like gear oil as there is no requirement for EP additives. Suspension oil too is perfectly fine. I do think that oil is better than grease.
What is FAR more important that what you use is how often you perform the maintenance. When I had a Totem Solo-air I found that I had to put oil on top of the air piston after each full day of riding at Whistler.

I think that you would be hard pressed to feel any difference between various oils for lubrication on top of the piston in a fork. Cheapest option is whatever engine oil you have sitting around for your car. Synthetic or regular oil, thick or thin, it is not going to matter. You don't need anything like gear oil as there is no requirement for EP additives. Suspension oil too is perfectly fine. I do think that oil is better than grease.
What is FAR more important that what you use is how often you perform the maintenance. When I had a Totem Solo-air I found that I had to put oil on top of the air piston after each full day of riding at Whistler.

Actually there are pretty significant differences in the lubricity of various oils - look for oils that are designed with the intention of lubrication primarily rather than damping. High quality damper oil usually priorities viscosity index (temperature stability) and anti-foaming over actual lubrication, whereas oils designed specifically for lubrication purposes (Fox Float Fluid and Fox 10wt Green fluid are my preferences) tend to be slipperier. Silicon-based grease (Slickoleum/Slick Honey) has the best short-term lubrication of rubber surfaces, but eventually gets displaced, which is why having a small amount of oil in the chamber with the piston is definitely a good thing.

However, on the Solo Air note - be aware that continually "topping up" the air chamber like that will end up with the oil making its way through the equalisation valve into the negative chamber, which has a tiny volume to begin with. This affects the feel of the fork substantially and makes it feel quite harsh at the top of the stroke.